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Learn Contest Math
Carefully designed for math contest students - available to everyone, for free.
Curated Resources
Learn new topics from a vetted list of high-quality resources. If one resource doesn't click, look at another!Explore Foundations Resources
| Math Resources | ||
|---|---|---|
| AoPS | Number Theory Basics | modular arithmetic, gcd, and classic lemmas |
| AoPS | Geometry Essentials | similarity, circles, power of a point |
| MATH | Combinatorics Toolkit | invariants, pigeonhole, and double counting |
| OLYM | Functional Equations | standard substitutions and symmetry tricks |
Extensive Problemsets
Practice each topic with extensive problemsets and solutions covering a wide range of difficulties.Go to Problems Page
| Source | Problem Name | Difficulty |
|---|---|---|
| AMC 10 | Modular Patterns | Easy |
| AIME | Counting Arrangements | Normal |
| USAMO | Geometry Chase | Hard |
| AoPS | Inequality Practice Set | Hard |
Progress Tracking
Use our progress-tracking tools to track your progress in the Guide and stay motivated.Open Dashboard
Modules Progress
12 total
Help when you need it
Ask questions, share solutions, and learn from other contest students in our Discord community.Visit Discord Community →
Contribute to the Community.
USAMO Guide is a student-run community dedicated to olympiad mathematics. Join us to write lessons, curate problem sets, and grow as a mentor alongside fellow contest enthusiasts.
Pranav Ramesh
Founder & CEO
Spursh Deshpande
CTO
Siddhant Arora
COO
Daniel Liao
CMO
Frequently asked questions
The essentials about the competition path, how the Guide works, and how to get involved.
- What are AMC, AIME, and USAMO?
These are the three big rungs of the US math competition ladder. AMC 8 is for middle schoolers, AMC 10/12 for high schoolers. While both are 25-question multiple choice contests, score well enough on them and you would qualify for AIME, a much harder 15-question numerical exam. Do well on the AIME aswell and you're at the USAMO (or USAJMO) territory. This would probably be the toughest math test most high schoolers will ever take. For official dates and registration, check the MAA competitions page.
- Is this an official syllabus?
Nope. USAMO Guide is built by the community, for the community. It's our best attempt at organizing what actually works for AMC/AIME/USAMO prep, not something blessed by the MAA :/ Think of it as notes that are passed down and refined by people who've been through the process, constantly getting better as more people chip in.
- I found a bug / typo / confusing explanation, what do I do?
Tell us! Hit "Contact Us" at the top of the page, or email [email protected]. If you're comfortable with GitHub, you can also open an issue directly on our GitHub repository , It's often the fastest way to get something fixed.
- I want live classes or one-on-one tutoring...
That's not really what we do.. We're a self-paced resource. For live instruction, AoPS runs solid online classes. If you still want structure and other people around, join one of our study groups or hop into a weekly mock contest for practice under real conditions.
- Do I need to already be good at math / qualified for USAMO to use this?
Not even close. Start on day one of AMC 8 prep or show up already grinding toward USAMO, either way, there's a place for you here. The material ramps from the basics up to olympiad-level, so you can jump in wherever you actually are.
- Where can I get help when I'm stuck?
Our Discord is the best place. People are usually around to help with a specific problem or concept. Beyond that, you can join a study group, get paired with a mentor, or just email us if it's a question about the guide itself.
- How can I contribute?
Please do. Fix a typo, rewrite a confusing explanation, add a problem, improve a diagram, clean up some code - it all helps. Head to our GitHub for contribution guidelines and open issues.
- Is this open source?
Yes, all of it! Fork it, build on it, poke around and see how it works. Nothing's hidden. (Attribution required + Commerical use not allowed.)